Distinct paper folding traditions arose in Europe, China and Japan which have been well-documented by historians. These seem to have been mostly traditions, until the 20th century.
In the China traditional funerals often include the burning of folded paper, most often representations of gold nuggets(yuanbao). The practice of burning paper representations instead of full-scale wood or clay replicas dates from the Sung Dynasty(905-1125C.E), through its not clear how much folding was involved. Traditional Chinese funeral practices were banned during the Cultural Revolution, so most of what we known Chinese paper folding comes from the modern-day continuation of these practices in Taiwan.
In Japan, earliest unambiguous reference to a paper model is an a short poem Ihara Saikaku in 1680 which mentions a traditional butterfly design used during Shinto weddings. Folding filled some ceremonials function in Edo period Japanese culture; noshi were attached to gifts, much like greeting cards used as today. This developed into a form of entertainment; the first two instructional books published in Japan are clear recreational.
In Europe, there was a well-developed genre of napkin folding, which flourished during the 17th and 18th centuries. After this period, this genre declined and was mostly forgotten; historian Joan Sallas attributes this to the introduction attributes this to the introduction of porcelain, which complex napkin folds as a dinner table status symbol among nobility. However, some of the techniques and bases associated with this tradition continued to be a part of European culture; folding was a significant part FREIDIRICH FROEBEL’s “Kindergardten” method, and the designs published in connection with his curriculum are stylistically are similar to the napkin fold repertoire.
When Japan opened its borders in the 1860’s, as part of modernization strategy, they imported Froebel’s Kindergarten system-and with it, German ideas paper about paper folding. This include the ban of cuts and the starting of a bicolored shape. These ideas, and some of the European folding repertiore, were integrated into Japanese tradition. Before these, traditional sources use a variety starting shapes, often had cuts; and if they have color or markings, these were added after the model folded.
In the early 1900’s Akira Yoshizawa, Kosho Uchiyama others began creating and recording original origami works. Akira Yoshizawa in particular was responsible for a number innovations, such as wet-folding and the Yoshizawa-Randlett diagramming system, in this work inspired a renaissance of the art form. During the 1980’s a number of folders started systematically studying the mathematical properties of folded forms, which led to a rapid increase in the complexity of origami models.
Origami 